In general, most form submissions can be captured through the "Form Submit" rule in Adobe Launch. You need to be able to identify the form:
Note: if the developer has suppressed the "form submit" action (and yes, that happens more than you would think), this will break your ability to detect the form submission.
Depending on what all you need to collect from the form (keep in mind, you shouldn't be using Adobe as a tool to collect "form data" (I've seen people try to use this to run contests, or other type of submission collection.. this is not the proper tool for this, and since there are many ways to "opt out" of analytics, you really should be using a proper DB to collect the results). However, you may need to collect form data for analytical purposes, such as tracking "search forms", etc...
The way the form is created will make some changes to how you collect the data, but you should be able to get data from the from via selectors... Complex form elements like multi-selection lists might be more difficult... I can't really go into details without knowing what you need and how the form is designed.
Or if you are working with a developer, you could have the developer code a data layer event, then instead of listening directly for the form submission, you can just use use this instead.... this would be the easiest for you, but would also probably be the slowest, since you will have to wait for the developers to do their work.